VARIATIONAL INEQUALITIES FOR PERTURBATIONS OF MAXIMAL MONOTONE OPERATORS IN REFLEXIVE BANACH SPACES

抄録

Let $X$ be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space $X^*$, and let $K$ be a nonempty, closed and convex subset of $X$ with 0 in its interior. Let $T$ be maximal monotone and $S$ a possibly unbounded pseudomonotone, or finitely continuous generalized pseudomonotone, or regular generalized pseudomonotone operator with domain $K$. Let $\phi$ be a proper, convex and lower semicontinuous function. New results are given concerning the solvability of perturbed variational inequalities involving the operator $T+S$ and the function $\phi$. The associated range results for nonlinear operators are also given, as well as extensions and/or improvements of known results of Kenmochi, Le, Browder, Browder and Hess, De Figueiredo, Zhou, and others.